Animals Made from 13 Circles (2016)
112 comments
·April 2, 2025DrNosferatu
KolibriFly
Feels like the mathematical version of "just because you can doesn't mean you should."
WorkerBee28474
Related: 'A meeting with Enrico Fermi' https://www.nature.com/articles/427297a
kbelder
"and with 20 billion I can make it hold a conversation."
NitpickLawyer
To paraphrase that quote about hydrogen: Give gradient descent a few billion parameters, and it starts wondering where it came from and what does it all mean.
kazinator
Bravo! HN Gold.
rob74
Looks more like an amoeba to me...
ezekg
It's really satisfying to create logomarks solely out of circles, idk why. A challenge, I guess.
I did a few back in my day as a designer:
1. https://dribbble.com/shots/1909369-Liberty-Eagle-Arms
2. https://dribbble.com/shots/1553151-Flint-mark-icons
That first one is some of my best work.
tuyiown
Constraints forces creativity. Some well chosen constraints are aesthetics rules that helps you land pleasing results. Poetry has a long history on that matter.
Another example of constrained creativity is early to mid nineties electronic music.
KolibriFly
There's something oddly meditative about designing within strict constraints like circles
jaredhallen
Yeah, those are all really nice. Good work.
rob74
> Inspired by the Twitter logo, which is made from 13 perfect circles
Compared to that, the new logo doesn't have a circle (segment) anywhere to be seen (unless you consider straight lines as circle segments with the center located at infinity of course), and is simply the "mathematical double-struck capital X" from an unknown but probably pre-existing font (apparently Monotype's "Special Alphabets 4" comes close, but isn't identical, according to https://tweethunter.io/blog/how-to-write-twitter-x-iphone-ma...).
enqk
Japanese family crests (Mon: 紋) are almost entirely made of circles (and lines, but that's rarer)
Often depicting slices of vegetables, animals..
From few circles to hundreds
sverhagen
It feels like I'm looking at the next so many Ubuntu backgrounds!
nonethewiser
Im curious what the process looks like to implement this. It seems like it would be easiest to start with the animal using only perfectly(?) curved lines and then complete them into circles after the fact. Although that seems kind of pointless and I imagine they start with circles. And I guess it would hard to have a curve from a perfect circle without the circle?
I just have a hard time imagining you start with circles, lay them down (resize as needed) and continue. I mean I guess that doesnt sound so crazy after I say it... it just seems like it would add a lot of extra noise to the image that would make it much harder to draw.
tarentel
I can't speak to this but I took a drawing class a long time ago. I'm not very good but it was a lot of drawing circles. When you see people freehand stuff it's kind of wild but that's not how people learn how to draw they're just very good at it from practice. Most of learning is drawing very basic shapes, usually circles, and erasing parts that don't make sense and continuing.
jihadjihad
> drawing very basic shapes, usually circles, and erasing parts that don't make sense
There's a hilarious Spongebob bit [0] where Squidward is teaching an art class, and he starts off in that exact manner of trying to draw a perfect circle, only to have Spongebob subvert the entire idea. The whole episode is artistic gold IMO.
tarentel
I do remember that. Sorry I can't find a better website but this is a similar joke.
https://www.reddit.com/r/restofthefuckingowl/comments/6f71jm...
tmountain
I have been practicing art a lot lately. You can draw just about anything using spheres, cubes, cylinders, and cones. You start off with the 2d versions.
tarentel
I stopped after a few classes but I was amazed at how good I got in a short amount of time after learning how to break stuff down which isn't something I really thought about before. By all metrics I'm still a pretty terrible drawer but prior to that stick figures would have been challenging.
barrenko
True, I did some amateur vector art (in Illustrator) and you basically have to compose objects out of basic shapes. It is truly highly meditative.
laurentlb
There's some information on: https://www.smashingmagazine.com/2017/01/illustrating-animal...
"While sketching, I kept track of the number of circles I was using, counting one for every curve." After sketching an animal, it should be easier to adjust the image by inserting/removing/moving circles.
nonethewiser
Awesome, thank you!
adamanonymous
There are some photos of sketches at the bottom of the page. Looks like they started with curves and turned them into circles later
nonethewiser
I suppose the thing the circle is really informing is the "perfectness" of the curve. You cant just draw in curves and extend it to a circle (wont be perfect). I guess Im not sure how you get "perfect" curves.
I suspect its a stencil or something. So in some sense the circle does exist first, even if they only draw the curve from it initially (before marking it up with the full circle after the fact).
PebblesRox
If I were trying to do something like this I would sketch it out first with imperfect curves and then worry about making it perfect once I was at the computer. It would look slightly different but I don’t think it would make that much of an impact in the initial design process.
KolibriFly
What's wild is how much clarity and personality you can get from that process. Instead of adding noise, it forces simplification, which actually helps with visual clarity
iamwil
I remember some post that I can find now, that demonstrated the twitter bird logo is also made from circles. All I can find is this reddit post now.
https://www.reddit.com/r/interestingasfuck/comments/txdimd/t...
neallindsay
That was referenced in the post as the impetus for making these. Unfortunately it just links to a Google search.
KolibriFly
Not sure how precise it really is, but it looks convincing enough to feel intentional
wwarren
It’s mentioned in the article under the images as the inspiration for this work
thesz
Because circles there also need operations over them (union, intersection or subtraction), it is a good example of low complexity art [1].
[1] https://en.wikipedia.org/wiki/Low-complexity_art
My son is a big fan of bytebeat [2], which is also a low complexity art, but music.
[2] https://dollchan.net/bytebeat/#4AAAA+kUryC/X0CixswNhQyM1Q01N...
apankrat
I did something similar 15+ years ago to use as an avatar in forums, twitters and some such - https://swapped.ch/#!/personal-mark
vismit2000
Reminds of 'Drawing with circles' in 3b1b classic on Fourier series: https://www.youtube.com/watch?v=r6sGWTCMz2k
So if we remove the condition of 13, everything is in fact made of circles only!
abeppu
See also work from Schmidhuber in the mid/late 1990s https://people.idsia.ch/~juergen/locoart/node12.html
ehaveman
wow, that's beautiful - the whole site https://people.idsia.ch/~juergen/ is an amazing rabbit hole im gonna lose myself in.
Etheryte
The red button is an absolute delight, be sure not to press it.
srean
He was done a great deal of injustice when he was passed over for the Turing award that was given to Hinton, Bengio, LeCun.
Then there is this from his blog --
Dec 2024: Sadly, the Nobel Prize in Physics 2024 for Hopfield & Hinton is a Nobel Prize for plagiarism. They republished methodologies developed in Ukraine and Japan by Ivakhnenko and Amari in the 1960s & 1970s, as well as other techniques, without citing the original papers. Even in later surveys, they didn't credit the original inventors (thus turning what may have been unintentional plagiarism into a deliberate form). None of the important algorithms for modern Artificial Intelligence were created by Hopfield & Hinton. Details in the recent technical report, with lots of references, links, and facts.
https://people.idsia.ch/~juergen/physics-nobel-2024-plagiari...
moralestapia
Agree.
Also, AlphaFold is great but hardly an innovation. David Baker deserved it 100%.
moconnor
I thought this was a joke, but he actually did do this first. Impressive!
seanhunter
I'm not sure whether or not he did this first, but it's very similar to an extremely impressive, but old and well-known illustration of the power of Fourier analysis in which you construct a "Fourier epicycle" (think: machine made of circular gears of different ratios) that can sketch any image. 3blue1brown has a great video on Fourier Epicycles but you can also get the idea here https://mathematica.stackexchange.com/questions/171755/how-c...
floxy
Also of potential interest is Kempe's Universailty Theroem which states you can draw any (polynomial) shape with a set of mechanical linkages. Like one that will sign your name.
https://academic.oup.com/plms/article/s1-7/1/213/1570315?log...
iamwil
Or check out drawing Homer Simpson with the same technique https://www.youtube.com/watch?v=QVuU2YCwHjw
fracus
Art with restrictions can be more interesting than without.
yesthisiswes
This is so true. I took a figure drawing class in college and we were instructed to draw with a cloth and charcoal dust. Easily some of the best work I made came out of that restriction.
PlunderBunny
Architecture too. The worst building come from architects given a blank page to start with. Constraints, and sympathy for the surrounding built environment produce great work.
Not exactly circles, but famously:
With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
https://en.m.wikipedia.org/wiki/Von_Neumann%27s_elephant